Question: Simplify the following expression: $ p = \dfrac{-3}{4} + \dfrac{y + 9}{-y + 4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-y + 4}{-y + 4}$ $ \dfrac{-3}{4} \times \dfrac{-y + 4}{-y + 4} = \dfrac{3y - 12}{-4y + 16} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{y + 9}{-y + 4} \times \dfrac{4}{4} = \dfrac{4y + 36}{-4y + 16} $ Therefore $ p = \dfrac{3y - 12}{-4y + 16} + \dfrac{4y + 36}{-4y + 16} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{3y - 12 + 4y + 36}{-4y + 16} $ $p = \dfrac{7y + 24}{-4y + 16}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-7y - 24}{4y - 16}$